Monolithic silicon rate-gyro with integrated sensors

ABSTRACT

A monolithic single crystal Si rate-gyro consisting of in the preferred embodiment, an outer torsional frame, self resonating with a substantial amplitude, as controlled by a four-terminal piezo torsion sensor, connected to an inner frame by torsional hinges. The inner frame itself is connected to a fixed inner post, by a set of torsion hinges, defining an axis of rotation perpendicular to the first axis. Rotation of the axis of oscillation of the outer body causes the moving mass and the inner frame to tilt and oscillate at the outer frequency due to Coriolis forces, thereby periodically deforming the inner hinges in torsion. These inner hinges are likewise equipped with a four-terminal piezo voltage torsion sensor, giving an indication of the rate of rotation of the sensor. The design allows for good sensitivity, due to the substantial swing of the outer oscillator, its high moment of inertia, excellent Si spring characteristics, and excellent sensitivity of the torsional sensors. Because of the integration of all of parts in silicon and its inherent simplicity, it can be made very inexpensively.

CROSS REFERENCE TO RELATED APPLICATION

This application is a continuation-in-part of prior application Ser. No.08/139,397, filed Oct. 18, 1993.

TECHNICAL FIELD

The invention relates to gyroscopes and accelerometers and, inparticular, to micromachined gyroscopes and accelerometers.

BACKGROUND ART

Vibratory gyroscopes provide a measure of the rate of rotation bysensing the effects of a Coriolis force on an oscillating body. Suchsensors are very interesting for a number of applications. Thoughlacking the precision of the rotary gyros, their price makes themattractive for many applications. One example is the automotive brakecontrol system, where the rate of rotation of the car needs to be sensedand controlled to avoid spin. Prices of many vibratory solid stategyros, using either quartz or piezo-electric materials are at present inthe $500 to $1500 range.

This price is excessive for many potential mass applications such asautomotive brake systems, robotic control, patient monitoring, virtualreality simulation, video games etc. These uses need another one or twoorders of magnitude in price reduction to make the product viable andrequire semiconductor fabrication techniques to achieve this priceperformance ratio.

Micromachined rate gyro sensors have been made in the past. U.S. Pat.No. 4,598,585, by B. Boxenhorn, assigned to Draper Laboratory, describesa micromachined planar inertial sensor, consisting of a pair of gimbals,positioned at right angles to each other. The inner gimbal plate carrieson it a substantial mass, which acts as the gyroscopic detector. Theouter gimbal, noted as the y-axis in the patent, is driven byelectrostatic forces (or electromagnetic forces), and is oscillating ina torsion mode, at a frequency equal to the torsional resonancefrequency of the inner gimbal. Rotation of the sensor around the z axiscauses the first oscillation to excite the inner resonance frequency,which is detected by a set of capacitive sensors on the inner gimbal.

The method is elegant in principle. In prior art devices, it has beensuggested that the gimbals may be made out of many materials, such assilicon dioxide, nitride, oxy-nitrides, or even stamped steel oraluminum sheets. During their deposition it is very difficult to producematerials with the right stress. As a result, the frequency of the innergimbal is not well determined and needs to be trimmed, in order to matchthe driving frequency. These materials are also subject to workhardening, hence the frequency of the inner resonance will change overtime, causing a mismatch with the driving frequency, and an apparentloss of sensitivity.

U.S. Pat. No. 4,699,006 by B. Boxenhorn discloses a vibratory digitalintegrating accelerometer, based on the same technology. In this case az axis acceleration causes a change in the resonant frequency around they axis. The changes in frequency are representative of the z axisacceleration.

U.S. Pat. No. 5,016,072 by Paul Greiff describes further improvements onthe technique. The dielectric layers of U.S. Pat. No. 4,598,585 havebeen replaced with a sheet of boron doped p+ silicon, and the asymmetricmass has been replaced by a symmetric one. Buckling of the oxide innerflexures causes undesirable large variations in the inner resonantfrequency; special flexure footings need to be provided. Flexure groovesare needed to give controllable stiffness in the flexure. The stress inthe boron doped material requires stress relief and trimming of thehinges. Electrostatic balanced force techniques are used to restrain themotion of the inner gimbal, to avoid cross-coupling and changes of itsresonant frequency. The outer axis needs to be driven at the resonancefrequency of the inner axis, which is done by dead reckoning, andrequires frequency trimming.

U.S. Pat. No. 5,203,208 by J. Bernstein also assigned to Draper Lab,describes a symmetric micromechanical gyroscope, also using boron dopedsilicon. Here the resonance frequencies of both axes are designed to bethe same, and trimmed to be identical. Trimming slots are also requiredto relieve stress in the boron doped silicon. As a result the drivevoltage can be vastly reduced, which substantially helps in theelimination of parasitic pick-up signals.

Boxenhorn and Greiff in Sensors and Actuators, A21-A23 (1990) 273-277have described an implementation of a silicon accelerometer, of the typedescribed in U.S. Pat. No. 4,598,585, mentioned above. Here the flexuresare made out of boron diffused silicon. They ascribe the difficultiesencountered with this approach due to the unknown pre-stress, which setsthe torsional stiffness and sensitivity of the device.

In all the above processes, the stresses in the hinge material areuncontrolled, and the frequencies unpredictable. An object of theinvention was to devise a low-cost micromachined gyroscope havingimproved frequency stability and which is easy to manufacture.

SUMMARY OF INVENTION

Many of the shortcomings of prior art micromachined gyroscopes areovercome by the use of stress free single crystal silicon for the hingesof the mass elements. One way to achieve this is by using Simox materialas the starting material. Single crystal silicon is an ideal hingematerial, as the material has no dislocations and does not work harden,which is very important since the hinge is continuously under very highcyclical stress. The properties and resonance frequencies arepredictable, no trimming slots are required. The Simox material alsoprovides for a well controlled etch stop. Alternatively, epitaxialmaterial, grown on a substrate of opposite doping can be used, togetherwith electrolytic etching, as is well known in the art.

When single crystal silicon is used for the hinges, very sensitive yetinexpensive four-point piezo voltage sensors can now be incorporated tomeasure the torsional displacement of the hinges. The plated mass isreplaced by silicon, in symmetric form if so desired. As a result thecomplexity and cost can be vastly reduced.

As compared to prior art designs, the preferred embodiment inverts thedriven and sensing axes. This allows for better use of the silicon. Thedriven axis is easily brought to resonance at its natural frequency.Because the great increase in sensitivity, the second axis need not bebrought to resonance, although it can be done if so desired. Because nowork hardening takes place, and since very little stress is present inthe silicon, the resonant frequencies are predictable and stable.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a top plan view of a micromachined device in accord with thepresent invention.

FIG. 2 is a sectional view taken along lines 2--2 in FIG. 1.

FIG. 3 is an enlargement of a torsional hinge of the device of FIG. 1,showing a torsion transducer.

FIG. 4 illustrates an alternate embodiment of the torsion transducershown in FIG. 3.

FIG. 5 is a partial cutaway plan view of a Simox wafer for fabricatingdevices of the present invention.

FIG. 6 is a side view of a plan for fabricating symmetric devices withthe present invention by means of wafer bonding.

FIGS. 7a and 7b illustrate magnetic drive structures for the device ofthe present invention.

FIGS. 8a and 8b illustrate an alternate drive configuration with drivenand sensing axes inverted.

FIGS. 9a and 9b illustrate torsion accelerometer devices in accordancewith the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

With reference to FIGS. 1 and 2, an outer silicon frame 101 oscillatesaround a pair of hinges (y-axis) 103, and is attached to an inner frame105, which itself is attached to a fixed inner post 109 with a set oftorsion hinges 107 (along the x-axis), at right angles to the first setof hinges. The outer frame is made to be self-oscillating, in a wellcontrolled amplitude, and is driven by either electrostatic or magneticforces e.g. using plates 113 which communicate electrostatic or magneticforce to the spaced apart outer frame. One or more built-in torsionsensor 111 in the silicon outer hinges provides the means forself-oscillation and amplitude stabilization.

Rotation of the system around the z axis causes the moving mass of theouter frame 101 and the inner frame 105 to oscillate at the outerfrequency around the inner hinges 107 due to Coriolis forces, therebyperiodically torsioning these hinges. The amplitude of the oscillationaround the inner hinges, is proportional to the rate of the imposed zaxis rotation. These inner hinges are also equipped with a similarfour-terminal piezo torsion sensor or a capacitive sensor 115, whichmeasures the deformation of the hinges, which is proportional to therate of rotation of the structure. Leads for the various sensors arebrought in from the fixed binding post 117; if necessary the transducercan be inverted 180 degrees and bonded directly to leads on the post.

The design allows for very good sensitivity, due to the large amplitudeof the outer oscillator, its large moment of inertia for a given chipsize, outstanding Si spring characteristics, and excellent sensitivityof the torsional sensor. As it turns out many of the desiredorientations for anisotropic Si etching coincide with those for optimaltorsion sensing. Because of the complete integration of all these partsin silicon, the device can be made very inexpensively. If necessary, theelectronic drive circuits could also be integrated.

Typically, the torsional resonance around the inner hinge is chosenhigher than the resonance of the outer hinge. It is possible to put theresonance frequency around the x-axis close to the resonance frequencyof the outer frame around the y-axis hinges. Hence if so desired, theexcursion obtained around the inner springs can be much larger than the"static" signal which would be obtained if no resonance took place. Thisis the feature which is used in the previous embodiments (except for theinversion of inner and outer axes); however it requires exact setting ofthe inner resonance frequency. The inner resonance frequency changes asthe outer frame rotates around the y axis, since this causes the momentof inertia along the x axis to change. Cross coupling will take place;to avoid this, it is better to separate the resonance frequencies if theincreased sensitivity is not needed.

The increase in sensitivity can be seen from the analytical expressionof the rate gyro equation:

    jφ+bφ+kφ=-hψ

where φ is the angle of the gyro (inner axis), j the moment of inertiaof the gyro, b the damping constant (if any is present) and k the springconstant of the inner hinges. ψ is the rate of rotation around the zaxis, h is the spin momentum, given by the product of Iω where I is themoment of inertia and ω the angular frequency of the oscillating body.For a rotating gyro, ω=dΘ/dt is often constant, but for a vibratorygyro, Θ is a sinusoidal function of time, and therefore so is the spinmomentum. If Θ=Θ₀ sin ωt then h=IΘ₀ ω cos ωt. Neglecting transienteffects and resonance conditions, the steady state solution for theangle is given by: ##EQU1##

The larger I, ω and Θ₀, and the smaller the spring constant k of theinner hinges, the larger the resulting deflection angle is bound to be.If we set the rate of rotation equal to unity, then we can look upon theabove expression as a figure of merit for the overall design. Since thetorsion sensors are really strain (or stress sensors) the quantity to beoptimized is maximum strain, which is slightly different, but not muchso, from the deflection. For a given die size of silicon it is foundthat the largest figure of merit is obtained by increasing I and Θ₀, theamplitude of oscillation. Increasing I usually lowers ω, but thisdecrease is vastly offset by the increase in I. It is for this reasonthat putting the oscillating mass on the outside provides for improveduse of the silicon real estate. The spring constant k cannot bearbitrarily lowered to increase sensitivity, since the inner hinges mustbe capable of supporting all the mass with a large safety factor forshock.

A typical design may have an outer square frame 101 dimension of 5 mm, awafer thickness of 500 microns, 800 micron widths for frames 101 and105, outer hinges 103 being 200 microns long, 80 microns wide, 10microns thick, inner hinges 107 of equal thickness, 175 microns long and100 microns wide, and a square inner post 1.4 mm on a side. This designgives a resonance frequency of about 133 Hz around the outer hinges, and150 Hz around the inner hinges. The calculated figure of merit is 0.001which means that a rotation rate of 1 rad/sec gives a deflection angleof 0.06 degrees, which is quite a large angle. A small fraction of thisangle can be readily detected by the torsion sensor.

The preferred torsion sensor (111, 115) is of the four terminal type asillustrated in FIG. 3 and similar to the type described by Pfann et al.,but optimized here for a hinge. See "Semiconducting Stress Transducersutilizing the Transverse and Shear Piezo Resistance Effects", W. G.Pfann and R. N. Thurston, Journ. Appl. Phys., Vol. 32, 10, pg. 2008,1961. Current is passed through terminals 121 and 123 perpendicular tothe flexure hinge length, and the output voltage is measured betweenterminals 125 and 127.

Torsion of the hinge gives rise to a change in the voltage betweenpoints 125 and 127. For torsion of the hinge, the stresses present arepure shear stresses, oriented parallel to the indicated currentdirection. The field generated in the perpendicular direction is givenby the expression:

    E=iρσπ

where E is the field, ρ the nominal resistivity of the material, i thecurrent density, σ the shear stress, and π the relevant element of thepiezoresistive tensor in the particular direction.

By orienting the sensor as illustrated, with the current perpendicularto the length of the hinge, the current section can be made as long asis desirable, and the generated voltage, which is the integral of thefield, should increase linearly with the length of the current section.In principle the generated voltage could exceed the applied voltage atthe current terminal, but in practice because of shorting due to thecurrent electrodes, the generated voltage never gets that high. In thispreferred arrangement, the geometry of the sensor matches perfectly thegeometry of the hinge.

Another orientation is illustrated in FIG. 4. Here the current isparallel to the hinge length from 131 to 133, and the voltage is pickedup perpendicular to the hinge length between terminals 135 and 137. Thefield generated is given by the same expression, but the current widthis now restricted to the width of the hinge. The only way to increasethe voltage here, is to increase the applied voltage at the currentleads. Note also that the first orientation of the torsion sensor isalso advantageous for another reason: the current supply lines areusually quite broad, and they leave little room to bring out the voltagesensing lines, if they are oriented as in FIG. 4. If the hinge is underconsiderable shear stress, then it is advantageous to put the currentcarrying lines at the edge of the hinge, where the shear stress is zero,as this reduces metal fatigue.

Silicon, in the right orientation, is extremely sensitive to shear, moreso than to any other stress. For a (100) orientation of the Si wafersurface, which is the preferred orientation for most micromachining, thehighest shear sensitivities are obtained with the torsion bar in the(100) direction for p type silicon, and in the (110) direction for ntype silicon. The piezo-resistance coefficients are almost independentof doping, until the resistivity reaches a value on the order of 0.01ohm-cm. Note that the output of this torsion sensor is independent ofany linear stresses or bending of the hinge. Instead of 4 contactpoints, (2 for current, 2 for voltage), the number can be reduced to 3,using one current injection and two symmetrically placed current pickuppoints.

The described piezo voltage is a bulk effect; however in many hinges ofinterest, the thickness of the hinge is much less than the width of thehinge. Since the shear stress reverses sign on the other face of thehinge, the generated voltages also reverse sign. The effects would thentend to cancel each other if the current were uniform throughout thethickness of the hinge. Therefore the applied current must be restrictedto one half of the hinge, where the shear stress has always the samesign. In practice it is best to restrict the current to the top fewmicrons of the hinge, as the stress is largest there, and to reduce thepower dissipation. This can be done by preferentially heavy doping ofthe top few microns (n-type in n-type material), or by junctionisolation (e.g., making an n type well in a p type substrate). Thelatter technique has the advantage that the sensor is electrically nolonger part of the hinge and the associated structures, but is nowjunction isolated and therefore much less sensitive to the drivingvoltage pickup.

To avoid DC offsets etc. and interfering noise at the driving voltages,the applied current to the torsion sensor can be AC, usually at afrequency higher than any of the resonant frequencies. The torsion thenproduces an amplitude modulation of the pickup voltage at the drivingfrequency, which can be readily demodulated, giving the desired signal.The output of the torsion sensor can be used in a positive feedbackscheme to resonate the oscillator at its resonant frequency, or used asa measure of the deflection of the hinge, or both.

For the fabrication, Simox wafers are preferred, although in principleany other silicon on insulator wafer, with a similar structure can beused. Epitaxially grown silicon, of a different type as its underlyingsubstrate can also be used together with electrolytic etching. What isrequired is a layer of high quality, stress free silicon separated fromthe bulk by a suitable etch stop. When the hinges are made out of thisSimox material, they are virtually stress free, and of very highquality. Simox wafers of the type shown in FIG. 5 consist of anepitaxial single crystal silicon layer 141, from a fraction of a micronto tens of microns thick, grown on top of an oxide layer 143. Underneaththe top Si layer 141 is a silicon dioxide layer 143, typically severalthousands of Angstroms thick, and which itself sits on top of the bulkof the silicon wafer 145. Other silicon on insulator structures can beused, equivalent in topography to Simox, but using different methods toproduce the structure.

When this wafer is used with orientation dependent etching such as KOHor EDA, the oxide provides for a very good, well controlled and cleanetch stop. Since the epi deposition gives rise to a uniform thicknesslayer, the thickness of the hinges, determined by the thickness of theepi, are very uniform in size all over the wafer. This property givesrise to a very uniform hinge thickness, which is critical to obtain auniform resonance frequency of all the devices on the wafer.

Typically the wafer is etched from the back, defining the variouscavities and masses, as is well known in the art, using the appropriateanisotropic etchant. For example, in FIGS. 1 and 2, frames 101, 105 andpost 109 are etched from the silicon wafer. Edge compensation can beused to protect the convex corners of the frames, if any are present.Etching of the corners is not critical, provided that all corners areetched symmetrically to preserve the symmetry of the mass. Aftercompletion of the bottom etch which goes through the bulk of the wafer,the epitaxial silicon is etched from the front, which defines the hingesand the outline of the plate. This can be done with an RIE chlorine etchor again using an anisotropic etch. The oxide is then removed, leavingthe mass and the hinges free-standing. Hinges 107 in FIGS. 1 and 2 arean example. The oscillating frame can be either the full thickness ofthe starting wafer, or alternatively, the thickness of the epi layer.The etching procedure steps may be reversed if so desired. No mass needsto be plated here; it is provided by the silicon itself, and can be verysubstantial.

Ohmic contacts for the torsion sensor on the hinge can belithographically defined, deposited and annealed in place as is wellknown in the state of the art using for example gold. The gold readilywithstands the etchants used. The contacts for the sensor are madebefore any deep lithography steps are done, since otherwise thepatterning becomes very difficult.

As outlined in FIG. 1, the device illustrated suffers from somecross-pendulosity. That is, the center of mass of the oscillator, andits rotation axis do not coincide. During the torsion oscillation, thecentrifugal forces created produce an excitation at double the frequencyof oscillation and may excite the vertical shaking mode of theoscillator. For that reason the mode spectrum of the oscillator shouldbe as clean as possible. The torsional resonance mode should be thelowest in the mode spectrum, and separated as much as possible from anyof the higher modes by at least 20% of the lower resonance frequency.Generally this is easier to do if the resonance frequency is low.

For the best performance, it is however possible to construct asymmetric oscillator using two wafers of the same thickness. In FIG. 6one processed Simox wafer 101 and a regular wafer 147 are bondedtogether, with their crystal orientations aligned. The Simox wafer isprocessed in the usual way, first forming the hinge pattern in theepitaxial layer and the joined lower frame portions in the main waferbody, i.e. those portions of the frame which are on the same plane asthe hinges and below. The wafer is then etched to remove excessmaterial. The second wafer is then bonded to the Simox wafer. A patterncorresponding to the upper portion of the frame, i.e. above the plane ofthe hinges, is masked and excess wafer material is etched away. TwoSimox wafers could be used, but this is not necessary. This can be donein a variety of ways as is known in the state of the art. By choosingwafers of the same thickness, an essentially symmetric structure can beobtained. The entire structure can be mounted in a vacuum enclosure. Theinner walls of the enclosure can be used to support the drivingelectrodes which are spaced from frame members.

It is highly desirable that the torsion oscillator be self-starting andself-oscillating, that is selecting its own natural resonance frequencyrather than having an externally imposed frequency. This is accomplishedby using a torsion sensor 111 of the above type in one of the y axishinges 103. Its output, demodulated if necessary, is then sufficientlyamplified and fed back with the right phase to the driving mechanism,either electrostatic or electromagnetic, to create enough positivefeedback to sustain oscillation at a controlled amplitude.Alternatively, the resonance condition of the outer oscillator can besensed by observing the linear strains in the inner torsion hinges. Therotation of the outer frame produces by reaction a periodic flexing ofthe inner hinges, which generates compressive and tensile stresses inthem. These can be picked up by common two terminal piezoresistiveelements. If the inner torsion hinges are oriented in the 110 direction,then n type material is not very sensitive to longitudinal stresses,although usable, while p type is. The best material for such dual use isp type material, oriented in the 110 direction. An n-type well in thismaterial will provide optimum sensing of torsion, while the p typematerial is optimum for tensile stresses. For a similar reason as above,the stress sensing is usually restricted to the top few micron. Thetorsion sensors are not sensitive to compressive and tensile stresses.

The excitation of the outer oscillator should be done as symmetricallyas possible, with a pull-pull arrangement 113 if done electrostaticallyas illustrated in FIG. 1. To this end magnetic excitation can also beused. This is schematically illustrated in FIGS. 7a and 7b. A coil 151is deposited on the outer frame 101, but isolated by a thin layer ofdielectric to avoid shorting, and current is passed through leads 153.Small permanent magnets 155 and a magnetic keeper 157, provide amagnetic structure, creating a B field 159. The interaction between thecurrent and the field causes forces 161 on the coil 151, giving rise toa torque 163, around the hinges 103. Because the structure is rathersmall, relatively large magnetic fields can be produced with inexpensivemagnets. The coil 151 is plated on the outer frame and returns throughone hinge. This drive method requires no high voltages as is needed forthe electrostatic drive, which not only makes the drive, but the pick-upof the small torsion signals more easy. The magnetic fields 159 shouldbe symmetric, including the fringing fields in the x direction. If not,the current interaction with this transverse field will produce torquearound the x-axis.

The electrostatic voltages needed for driving can be greatly reduced, ifthe gyro is operated in vacuum. Because the Q has been observed to beclose to 1 million, the driving voltages can be readily reduced to abouta volt. Because the driving forces are then negligible, as compared tothe inertia of the rotating mass, symmetry of the drive becomesunimportant. The mode spectrum also tends to be purer in vacuum.Inexpensive vacuum enclosures can be made through micromachining andwafer bonding techniques.

The detection scheme on the inner axis can be operated two ways: eitheras a straight sensor or as a force feedback scheme. The latter is wellknown to be in principle preferable as it reduces the cross coupling,but requires more complex electronics. As the device is plentysensitive, the same benefit can be accomplished to some degree bystiffening the inner hinges and reducing the excursion; this reduces thecross-coupling effects. Force feedback can be accomplished using eithermagnetic or electrostatic forces. The first one may be desirable, butcan only be used if electrostatic forces are used for the driving,because crossed magnetic fields cause interaction.

The preferred mode has been described as one where the inner mass 109 isfixed, and the outer frame 101 moving. As shown in FIGS. 8a and 8b, itis also possible to position the substantive mass 171 on the inner frame173, oscillate the mass around the inner x axis hinge 175 in acontrolled amplitude, with a positive feedback, and detect tilts on theouter y axis hinge 177, using sensor 179 and either force feedback orregular sensing mode. Driving the inner axis 175 (either electricallywith plates or magnetically), using the torsion sensor 181 allows themass 171 to be driven at its own resonance frequency, with a wellcontrolled amplitude. This is less efficient in terms of the factor ofmerit than the first mode, but it makes the lead contact problemsomewhat easier. Resonance frequencies around both axes can be selectedto be coincident, to increase the sensitivity of the system, but subjectto the above mentioned limitations.

Alternatively, both the configuration of U.S. Pat. Nos. 4,598,858 and5,016,092 can be executed using the Simox silicon hinge and massmaterial and the described torsion sensors instead of the capacitivepickups. In this mode the substantive mass is put at the inner x-axisgimbal, and is driven, magnetically or electrostatically, around theouter axis, nominally at the resonance frequency of the inner axis.Excitation of the inner axis resonance occurs when the sensor rotatesaround the z axis. As is the case in these patents, the x-axis isnormally not excited, and therefore cannot be used for setting thefrequency of the y drive. Dead reckoning must be used. Any drift betweenthe driving frequency and the resonance frequency causes an apparentloss of sensitivity. However, many of the problems encountered areovercome by the use of the stress free silicon material, which also hasno work hardening. Stabilization of the oscillation amplitude around they axis, driving it at resonance and pickup around the x axis is againmost cost effectively done with four-point piezosensors, and the hingesshould be made out of single crystal silicon.

It is also possible to apply these hinge technologies for production ofaccelerometers of the type first proposed by Boxenhorn in U.S. Pat. No.4,598,585. We propose that the hinges be made out of the single crystalmaterial as described, and that the sensor be of the four-terminal piezovoltage type as described. A preferred embodiment is illustrated in FIG.9, using a current loop as the actuator and sensor 193 for the feed-backsystem. B field 199 is created by an external structure as above;interaction with current loop 191 causes forces 201, producing torquearound hinge 197, which itself connects plate 203, carrying eccentricmass 195, to frame 205. This produces a force feedback accelerometer ofvery simple and inexpensive design and linear output. The unbalancedmass 195 is created here by etching. The weight, hinge and magneticfield are all uncritical; a simple calibration can be done by holdingthe accelerometer flat and then inverting it; this produces a 2 gacceleration. The current which is necessary to keep the unbalanced massin place, as measured by a zero output signal from the torsion sensor193, is a measure of the acceleration which the sensor is subjected to.

As drawn, the signal from the accelerometer is in principle derived froman acceleration in the z axis, but acceleration in the x-axis also givesa small, undesirable output signal, as the center of mass is not in theplane of the hinges. By using two identical devices as illustrated, inFIG. 8 and putting their output in opposition, it becomes possible toeliminate the spurious effects of cross-accelerations, while at the sametime doubling the output signal. The same current source can inprinciple be used to drive both sensors, but the voltages of the sensoroutputs can only be added after removal of the common mode signal. Themass unbalance can be created by making one arm longer than the other,or by removing the mass completely from one arm. The latter may be moreadvantageous, as it is lighter, and produces less stress on the hingeswhen high g forces arise. The output signal is the current needed tokeep the hinge 113 undeflected, and is linearly related to the z axisacceleration. A substantial symmetric mass can also be obtained by waferbonding, as defined above.

The device can also be made by using an electrostatic field to keep theplate in place, as is common for most feedback accelerometers. However,in order to avoid large voltages, the plate needs to be very close,which makes the design difficult. The magnetic approach does not sufferfrom this difficulty; also the homogeneity of the magnetic field is ofno concern, since the hinge never tilts, as restricted by the servoloop. Usually a single current loop, one turn coil 191, is adequate toprovide the necessary restoring force, so that no overlap of the coilwinding is necessary. Force (or torque) feedback accelerometers havegenerally superior performance as compared to other devices, especiallyfor low frequencies, but their cost is generally quite high. Theproposed system is a low cost version, which preserves most of theperformance characteristics, while drastically lowering cost. For thedevice as illustrated in FIG. 9, with a 2 mm eccentric mass, 500 micronsthick, 2 mm wide, and silicon hinges 10 microns thick, 70 microns wideand 400 microns long, the resonance frequency is on the order of 180 Hz,and with a 1000 Gauss external magnetic field, the current for 0.1 gacceleration is 10 mA, for a single turn loop, a readily measured value.The torsion sensor 193 is again of the four-terminal piezo voltage type;its output is now maintained at zero by the feedback loop.

We claim:
 1. A vibratory gyroscopic silicon transducer, comprising,asilicon micromachined inner post, having a top surface defining an x-yplane, a first silicon frame, surrounding the post, a first set ofsingle crystal silicon hinges connected between the first silicon frameand the inner post, with the hinges defining a first axis, a secondsilicon frame, surrounding the post and the first frame, the secondsilicon frame having a natural resonant frequency, a second set ofsingle crystal silicon hinges connected between the first and secondsilicon frames, defining a second axis at right angles to the firstaxis, the second frame defining a vibratory mass, at least onefour-terminal piezo voltage sensors, incorporated into at least one ofsaid first set and at least one of said second set of hinges, each ofsaid piezo sensors having at least two spaced apart current electrodeson the surface of the hinges making ohmic contact to an adjacent layerof silicon with an area of the silicon between the current electrodesdefining a resistive element, said electrodes positioned to transmitcurrent through said resistive element along a vector, the sensors alsohaving at least two spaced apart voltage sensing electrodes disposedalong a line generally perpendicular to said vector, means for measuringa voltage between said two spaced apart voltage sensing electrodes,means for increasing a density of a current flow in the resistiveelement so that the current flow density is at least doubled, wherebyshear forces present in each of the first and second set of hinges altera resistivity of the resistive element generating a voltage indicatingtorsion force, and drive means to make the second silicon frameoscillate at the natural resonant frequency around the second axis at aconstant amplitude, with a piezo sensor attached to a hinge of thesecond set of hinges providing positive feedback to control a frequencyat which the second silicon frame oscillates.
 2. The apparatus of claim1 wherein said inner post is fixed and said current electrodes areelongated, having a length generally perpendicular to the axis of saidfirst and second set of hinges.
 3. The apparatus of claim 1 wherein saidcurrent electrodes are elongated, having a length generally parallel tothe axis of said first and second set of hinges.
 4. The apparatus ofclaim 1 further defined by electrical leads connected to said electrodesand insulated from said silicon.
 5. The apparatus of claim 4 whereinsaid axis of said first and second set of hinges is aligned in eitherthe <100> direction or the <110> direction of silicon.
 6. The apparatusof claim 5 wherein said means for increasing the density of current flowcomprises a junction isolation region.
 7. The apparatus of claim 5wherein each hinge of said first and second set of hinges includes piezoresistive means for measuring longitudinal and bending stresses.
 8. Avibratory gyroscopic silicon transducer, comprising,a fixed siliconmicromachined inner post, having top surface defining an x-y plane, afirst silicon frame, surrounding the post, a first set of single crystalsilicon hinges connected between the first silicon frame and the innerpost, the hinges defining a first axis, with the first silicon frameattached thereto for movement about the first axis, a second siliconframe, surrounding both the post and the first frame, the second siliconframe having a natural resonant frequency, a second set of singlecrystal silicon hinges connected between the first and second siliconframes, defining a second axis at right angles to the first axis, thesecond frame attached thereto for movement about the second axis,defining a vibratory mass, at least one four-terminal piezo voltagesensors, incorporated into at least one of said first set and at leastone of said second set of hinges, each of said piezo voltage sensorsincluding a resistive element defined by a nominal resistivity of thecrystal silicon hinges to sense torsion in said hinges in which thepiezo sensors are incorporated, drive means to make the second siliconframe oscillate at the natural resonant frequency around the second axisat a constant amplitude, with at least one of said piezo sensorsattached to a hinge of the second set of hinges providing positivefeedback to control a frequency at which the second silicon frameoscillates.
 9. The apparatus of claim 8 wherein said drive means iselectrostatic.
 10. The apparatus of claim 8 wherein said drive means ismagnetic.